Computer data modelling, such as for data embodying a spatial representation of a desired characteristic, is frequently useful in fields such as mining and environmental sciences. In the case of mining as an example, it is oftentimes desirable to determine a representation of the spatial distribution of minerals and ores within a body of earth to model and predict the geometry and geology of material in the ground. The in-ground model can then be used for mine planning, drill hole location, drilling operations, blasting, excavation control, direction of excavated material and resource management, amongst other things.
To model an in-ground ore body, for example, sample data can be generated from measurements of mineral concentrations, or related quantities, at discrete locations within a three-dimensional spatial domain including the ore body. The sample data can then be analysed and, using a method of interpolation, synthesised into a model that can be used to make predictions of mineral concentrations at spatial locations distinct from those that were measured. A mathematical technique that has been found useful in this application is regression using the Gaussian process (GP) which is a stochastic process based on the normal (Gaussian) distribution and can be used to good effect as a powerful non-parametric learning technique for spatial modelling. Described by an appropriate covariance function, the GP can be used to infer continuous values within the spatial domain from the distribution of sample measurements. GPs and their application are described in Gaussian Processes for Machine Learning (MIT Press, 2006) by C. E. Rassmussen and C. K. I. Williams, the contents of which are incorporated herein by reference.